# Stored data for newform 98.6.a.f, downloaded from the LMFDB on 08 December 2025.
{"Nk2": 3528, "analytic_conductor": 15.717614341672101, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [7, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [98, 1, [3], [1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 520, "field_disc_factorization": [[2, 3], [5, 1], [13, 1]], "field_poly": [-130, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-471, -14, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22517998237515874, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "98.6.a.f", "level": 98, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 7], "level_radical": 14, "minimal_twist": "14.6.c.b", "nf_label": "2.2.520.1", "prim_orbit_index": 1, "qexp_display": "q-4q^{2}+(7+\\beta )q^{3}+2^{4}q^{4}+21q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "98.6.a", "trace_display": [-8, 14, 42, 0], "trace_hash": 2121326082977039618, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.926", "prec": 17}, {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "9.393", "prec": 17}, {"__RealLiteral__": 0, "data": "0.901", "prec": 17}, {"__RealLiteral__": 0, "data": "64.761", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, -8, 14, 32, 42, -56, 0, -128, 652, -168, -294, 224, 140, 0, 294, 512, -1302, -2608, 1442, 672, 0, 1176, 2646, -896, -5368, -560, 15722, 0, 1668, -1176, 14798, -2048, 19782, 5208, 0, 10432, 5182, -5768, -5260, -2688, 5124, 0, -4520, -4704, 13692, -10584, 14994, 3584, 0, 21472, 9606, 2240, 24006, -62888, -6174, 0, -42946, -6672, -38850, 4704, 23618, -59192, 0, 8192, 2940, -79128, 32002, -20832, -90678, 0, -89376, -41728, 47138, -20728, -37576, 23072, 0, 21040, -40970, 10752, 139858, -20496, -68376, 0, -27342, 18080, 55356, 18816, -123102, -54768, 0, 42336, 25586, -59976, 30282, -14336, 43652, 0, 209916, -85888, 4914, -38424, 298298, -8960, 0, -96024, -129474, 251552, -68018, 24696, 429394, 0, -27876, 171784, 55566, 26688, -41720, 155400, 0, -18816, 179756, -94472, -631812, 236768, -243978, 0, -57488, -32768, -381080, -11760, -224406, 316512, 0, -128008, 330162, 83328, -78426, 362712, 282968, 0, 532398, 357504, -151620, 166912, 35028, -188552, 0, 82912, -498474, 150304, -363422, -92288, -162372, 0, 310758, -84160, 161210, 163880, -137718, -43008, 0, -559432, 674182, 81984, 415422, 273504, -62328, 0, -695346, 109368, -272468, -72320, -848526, -221424, 0, -75264, -1273470, 492408, 626634, 219072, -521164, 0, 608366, -169344, 108822, -102344, 584514, 239904, 0, -121128, -674706, 57344, 1294342, -174608, -110460, 0, 311604, -839664, 696878, 343552, -1719746, -19656, 0, 153696, 107604, -1193192, -666204, 35840, -1325814, 0, -901832, 384096, -1237152, 517896, -94920, -1006208, 0, 272072, 1078766, -98784, -203460, -1717576, 932624, 0, -1749968, 111504, 535878, -687136, 1517306, -222264, 0, -106752, 436038, 166880, 314874, -621600, -1356950, 0, 1282392, 75264, 289730, -719024, 3113600, 377888, 0, 2527248, 419180, -947072, 58008, 975912, 1980720, 0, -2682162, 229952, 201726, 131072, -271446, 1524320, 0, 47040, 1155288, 897624, -1983030, -1266048, 504126, 0, 848046, 512032, 345114, -1320648, 2349242, -333312, 0, 313704, 789096, -1450848, 1720294, -1131872, 3732148, 0, 2346444, -2129592, 3175718, -1430016, -901866, 606480, 0, -667648, -1655152, -140112, -3968836, 754208, 2977044, 0, -815850, -331648, 1641906, 1993896, 840420, -601216, 0, 1453688, 645918, 369152, 495978, 649488, 1179416, 0, 2609126, -1243032, -1746234, 336640, 3165554, -644840, 0, -655520, -2008434, 550872, 672084, 172032, -7305438, 0, -1893462, 2237728, -375760, -2696728, -4057886, -327936, 0, -1661688, 4030006, -1094016, 7193012, 249312, 672042, 0, -2834132, 2781384, -4956252, -437472, -3813306, 1089872, 0, 289280, -1904238, 3394104, -77502, 885696, -4443460, 0, -28900, 301056, 2106426, 5093880, -1876896, -1969632, 0, -2506536, -4338498, -876288, -1207476, 2084656, -5162668, 0, 989898, -2433464, 92582, 677376, -7677096, -435288, 0, 409376, 2918062, -2338056, -1707846, -959616, -145320, 0, 1015360, 484512, -10274096, 2698824, 2783970, -229376, 0, -5177368, -6365680, 698432, -4889778, 441840, -3688146, 0, 354198, -1246416, -860370, 3358656, -710374, -2787512, 0, -1374208, 810582, 6878984, 1503860, 78624, 2937018, 0, 7493766, -614784, 105434, -430416, -7319382, 4772768, 0, 2664816, -1435896, -143360, -902104, 5303256, 6537720, 0, -3077948, 3607328, 10872204, -1536384, 3494568, 4948608, 0, -2071584, 1384740, 379680, 7341570, 4024832, 1380932, 0, 1162476, -1088288, 7476966, -4315064, 5810210, 395136, 0, 813840, -3058578, 6870304, -2585142, -3730496, 3674202, 0, 3615564, 6999872, -14774508, -446016, 8179486, -2143512, 0, 2748544, 2214286, -6069224, -6846702, 889056, 3090108, 0, 167392, 427008, 537306, -1744152, -2194374, -667520, 0, -1259496, 10245110, 2486400, -6673800, 5427800, -3870328, 0, 3545316, -5129568, 12130902, -301056, -1995980, -1158920, 0, 2876096, 916692, -12454400, -4502, -1511552, 17932474, 0, -2157984, -10108992, -299628, -1676720, 4408236, 3788288, 0, -232032, 10265734, -3903648, -12423336, -7922880, -2089248, 0, 103194, 10728648, -5741022, -919808, 6268458, -806904, 0, -524288, 1735322, 1085784, 6264258, -6097280, 6772122, 0, -19162242, -188160, -4900686, -4621152, -9444190, -3590496, 0, 7932120, -11037498, 5064192, 2093972, -2016504, -26686380, 0, 4364760, -3392184, -2718954, -2048128, 16551318, -1380456, 0, 5282592, -4411754, -9396968, 22285292, 1333248, -1428378, 0, -775136, -1254816, 13902028, -3156384, -1025052, 5803392, 0, -6881176, 9017274, 4527488, 16972686, -14928592, 1780240, 0, -12878082, -9385776, 6716766, 8518368, -585396, -12702872, 0, 5720064, -11366706, 3607464, -5711270, -2425920, 1414098, 0, -7101864, 2670592, 3952130, 6620608, 7182154, 560448, 0, 15875344, -9949842, -3016832, -876120, -11908176, -8676024, 0, 14647358, 3263400, -4938612, 1326592, 1076922, -6567624, 0, -7975584, 7670546, -3361680, 15053754, 2404864, -4220524, 0, -16779988, -5814752, 3774876, -2583672, -21876862, -1476608, 0, -1983912, -1515060, -2597952, -21532706, -4717664, -13268052, 0, -6003972, -10436504, -2722258, 4972128, 1035006, 6984936, 0, -1346560, 11651462, -12662216, 14262822, 2579360, 3702678, 0, 28696384, 2622080, -5876024, 8033736, -1207248, -2203488, 0, -2688336, -37697856, -688128, 10297950, 29221752, -8222536, 0, -8002680, 7573848, 32400102, -8950912, -15320970, 1503040, 0, 10786912, 10107822, 16231544, -4712526, 1311744, 25850188, 0, -18245352, 6646752, -26188918, -16120024, 3948420, 4376064, 0, -28772048, -2379636, -997248, -26830672, -2688168, 5831994, 0, 8698252, 11336528, -42197848, -11125536, 12626586, 19825008, 0, 1749888, 56769306, 15253224, -857814, -4359488, -1646946, 0, 33397142, -1157120, 3514980, 7616952, -2734774, -13576416, 0, 310008, 5942328, -3542784, -15353964, 17773840, 3358026, 0, -7423044, 115600, -16312898, -1204224, 11180358, -8425704, 0, -20375520, -20652482, 7507584, -28338460, 7878528, 27767754, 0, -3184020, 10026144, 38198664, 17353992, 2898042, 3505152, 0, 4829904, 21696590, -8338624, -4476912, 20650672, 13772192, 0, 56478826, -3959592, -3347400, 9733856, -9420334, -370328, 0, -2709504, -45523254, 30708384, 2482906, 1741152, -5277580, 0, 14086848, -1637504, -10467954, -11672248, -14777616, 9352224, 0, 6831384, -9730418, 3838464, -3525840, 581280, -7631862, 0, 5098132, -4061440, 26171586, -1938048, 17136042, 41096384, 0, -10795296, -3409812, -11135880, 3289620, 917504, -11292652, 0, -42715962, 20709472, 9392082, 25462720, -39717832, -2793728, 0, 19559112, 37746084, -1767360, 296352, 14752584, 21018228, 0, 3385410, -1416792, -17329522, 4985664, -10190250, 3441480, 0, -13434624, -1004980, 2841496, -2892078, 11150048, 7042140, 0, -2067174, 5496832, -16194612, -3242328, 8795514, -27515936, 0, -6015440, -70261482, -314496, -8886882, -11748072, -42992824, 0, -23556826, -29975064, 14157822, 2459136, 14562520, -421736, 0, 1721664, 1262694, 29277528, 8614138, -19091072, -53094888, 0, 25950552, -10659264, -11454478, 5743584, 11561578, 573440, 0, 3608416, -1308888, -21213024, 102209078, -26150880, 49011312, 0, -37796626, 12311792, -37432332, -14429312, -14602266, -43488816, 0, 6145536, -5247814, -13978272, -34421814, -19794432, -35055748, 0, -5721828, 8286336, -1481214, -5538960, -15898414, -1518720, 0, -29366280, 4912758, -16099328, -17819046, -5523728, -35959504, 0, -16450770, -4649904, 13902700, 4353152, -45611048, -29907864, 0, 17260256, 24665206, -23240840, 51889548, -1580544, -38161956, 0, 17952856, -3255360, -26742870, 12234312, 31033842, -27481216, 0, 10340568, 104496714, 14921984, -10988766, -14696808, 13159314, 0, -10016580, -14462256, 9065532, -27999488, -21131586, 59098032, 0, 1784064, -10944444, -32717944, 15171010, 8574048, 10163244, 0, -36347040, -10994176, 21320712, -8857144, 12775686, 24276896, 0, 27386808, -30023714, -3556224, 44797352, -12360432, -2587200, 0, -13908488, -669568, 104539708, -1708032, 27462834, -2149224, 0, 6976608, -65347878, 8777496, 12274794, 2670080, 6570956, 0, 3314078, 5037984, -31076598, -40980440, 76885452, -9945600, 0, 26695200, -27649290, -21711200, -1193140, 15481312, 68277762, 0, 58266156, -14181264, -14168826, 20518272, 16498188, -48523608, 0, 1204224, 58082100, 7983920, -131796204, 4635680, 27181182, 0, -26886656, -11504384, 34771926, -3666768, 37468746, 49817600, 0, 18008, 14117840, 6046208, 1595430, -71729896, 54000954, 0, -72318508, 8631936, 41025726, 40435968, 6543684, 1198512, 0, 6706880, 30711240, -17632944, 1225930, -15153152, 57148042, 0, 14634438, 928128, 71308202, -41062936, 111890422, 15614592], "weight": 6, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [-4, 0], [7, 1], [16, 0], [21, 0], [-28, -4], [0, 0], [-64, 0], [326, 14], [-84, 0], [-147, 21], [112, 16], [70, -6], [0, 0], [147, 21], [256, 0], [-651, 18], [-1304, -56], [721, -51], [336, 0], [0, 0], [588, -84], [1323, -105], [-448, -64], [-2684, 0], [-280, 24], [7861, 181], [0, 0], [834, 42], [-588, -84], [7399, -75], [-1024, 0], [9891, 0], [2604, -72], [0, 0], [5216, 224], [2591, 378], [-2884, 204], [-2630, 28], [-1344, 0], [2562, -642], [0, 0], [-2260, -336], [-2352, 336], [6846, 294], [-5292, 420], [7497, 411], [1792, 256], [0, 0], [10736, 0], [4803, -525], [1120, -96], [12003, -294], [-31444, -724], [-3087, 441], [0, 0], [-21473, 364], [-3336, -168], [-19425, -963], [2352, 336], [11809, 426], [-29596, 300], [0, 0], [4096, 0], [1470, -126], [-39564, 0], [16001, -1869], [-10416, 288], [-45339, 588], [0, 0], [-44688, -588], [-20864, -896], [23569, 720], [-10364, -1512], [-18788, -2684], [11536, -816], [0, 0], [10520, -112], [-20485, -1029], [5376, 0], [69929, 5726], [-10248, 2568], [-34188, 516], [0, 0], [-13671, 378], [9040, 1344], [27678, 1128], [9408, -1344], [-61551, 1644], [-27384, -1176], [0, 0], [21168, -1680], [12793, 6874], [-29988, -1644], [15141, -1071], [-7168, -1024], [21826, -4110], [0, 0], [104958, 4788], [-42944, 0]]}